XXVII.—On Fermat's Theorem

H. F. Talbot
1857 Transactions of the Royal Society of Edinburgh  
It is well known that no satisfactory demonstration has ever been given of Fermat's celebrated theorem, which asserts that the equationan=bn+cnis impossible, ifa,b,c, are whole numbers, andnis any whole number greater than 2. In Legendre'sThéorie des Nombres, he demonstrates the cases ofn= 3,n= 4, andn= 5, the latter only in his Second Supplement. In Crelle'sMathematical Journal, ix. 390, M. Dirichlet, a mathematician of Berlin, has demonstrated the case ofn= 14, but I am not aware whether his
more » ... aware whether his demonstration is considered successful. Legendre informs us (Second Supplement, p. 3) that the Academy of Sciences, with the view of doing honour to the memory of Fermat, proposed, as the subject of one of its mathematical prizes, the demonstration of this theorem; but the Concourse, though prolonged beyond the usual term, produced no result.
doi:10.1017/s008045680003221x fatcat:ihulwiayhbdxfehq35wgmc5ftu